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Groups > comp.ai.philosophy > #18797 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-08-08 12:15 -0500 |
| Last post | 2019-09-11 17:31 -0700 |
| Articles | 20 on this page of 244 — 17 participants |
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Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-08-08 12:15 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-08-08 21:28 +0100
Re: Provably unprovable eliminates incompleteness Dhu on Gate <campbell@neotext.ca> - 2019-09-08 06:06 +0000
Re: Provably unprovable eliminates incompleteness Stuart Redmann <DerTopper@web.de> - 2019-09-09 11:30 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 10:01 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-09 21:38 +0100
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 18:05 -0500
Re: Provably unprovable eliminates incompleteness David Brown <david.brown@hesbynett.no> - 2019-09-10 09:01 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-10 10:38 -0500
Re: Provably unprovable eliminates incompleteness David Brown <david.brown@hesbynett.no> - 2019-09-10 22:01 +0200
Re: Provably unprovable eliminates incompleteness [ Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-10 20:12 -0500
Re: Provably unprovable eliminates incompleteness Reinhardt Behm <rbehm@hushmail.com> - 2019-09-11 15:31 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:04 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Reinhardt Behm <rbehm@hushmail.com> - 2019-09-12 10:20 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 23:51 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Keith Thompson <kst-u@mib.org> - 2019-09-12 01:22 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:05 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 18:32 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 20:03 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 20:59 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 22:16 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 11:14 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-12 21:00 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-12 21:39 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-13 11:48 -0500
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 13:09 -0500
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 19:24 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-14 21:33 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 10:17 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:26 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 10:36 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 10:06 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:22 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 10:38 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:59 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 11:10 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 13:27 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 12:34 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 14:19 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 13:35 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 14:51 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 14:15 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 16:18 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 16:00 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 15:29 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 18:14 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Jeff Barnett <jbb@notatt.com> - 2019-09-16 23:34 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 14:25 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 16:21 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 16:01 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 15:46 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 18:07 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Me <invalid@invalid.de> - 2019-09-17 01:09 +0200
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 02:33 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 20:53 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:55 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 19:21 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:40 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 21:38 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 00:24 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 11:39 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:38 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 13:17 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Keith Thompson <kst-u@mib.org> - 2019-09-17 11:13 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 13:29 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) peteolcott <Here@Home> - 2019-09-17 11:20 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 10:56 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 11:29 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:32 +0100
Re: Cantor was wrong about cardinality --- (Correction) peteolcott <Here@Home> - 2019-09-17 12:49 -0500
Re: Cantor was wrong about cardinality --- (Correction) Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 19:59 +0100
Re: Cantor was wrong about cardinality --- (Correction) peteolcott <Here@Home> - 2019-09-17 14:09 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-17 11:42 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 14:01 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 17:51 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 15:58 -0500
Re: Cantor was wrong about cardinality --- (Mike Terry Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:46 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:52 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:55 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Keith Thompson <kst-u@mib.org> - 2019-09-19 14:44 -0700
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 17:31 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:02 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 20:01 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 22:39 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-17 22:23 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Keith Thompson <kst-u@mib.org> - 2019-09-18 01:39 -0700
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 09:59 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-18 09:21 -0600
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 10:41 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Keith Thompson <kst-u@mib.org> - 2019-09-18 13:55 -0700
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 16:17 -0500
Re: Cantor was wrong about cardinality --- [ CONCURRENCE ] peteolcott <Here@Home> - 2019-09-18 11:10 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 09:05 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 10:49 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 10:02 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:18 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 23:24 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 10:01 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:13 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:56 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:40 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 11:03 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 12:48 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 12:25 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 22:35 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 16:42 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:28 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 11:34 -0500
Re: Cantor was wrong about cardinality --- COMPLETE (Andy Goofed) peteolcott <Here@Home> - 2019-09-14 18:00 -0500
Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) peteolcott <Here@Home> - 2019-09-16 09:42 -0500
Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:13 -0600
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 19:36 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 21:38 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-16 10:21 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-14 00:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 10:26 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 18:24 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 22:19 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 21:23 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 22:31 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 22:04 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 23:21 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 22:40 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 00:27 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 23:55 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 00:59 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 00:12 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 10:15 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 09:35 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 11:00 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 10:14 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 11:26 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 10:42 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 13:10 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 12:36 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 13:49 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 12:59 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 14:12 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 13:30 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 14:45 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 14:14 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 15:29 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 14:38 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 15:56 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 20:38 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 22:03 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 21:33 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:35 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 11:42 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 12:43 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:24 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 23:32 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 23:21 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 17:13 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 19:49 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 09:45 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Don Stockbauer <donstockbauer@hotmail.com> - 2019-09-27 07:24 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-12 22:07 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-12 18:53 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-12 17:47 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-13 08:14 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-13 09:35 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-13 15:55 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 13:35 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 22:52 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:18 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 23:30 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:42 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Jeff Barnett <jbb@notatt.com> - 2019-09-14 18:12 -0600
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-15 08:09 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:50 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:13 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 11:24 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:30 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 12:08 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 18:15 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 13:35 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 20:02 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 14:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 22:26 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:11 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:12 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:11 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-17 21:10 +0200
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 14:30 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 14:33 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] Keith Thompson <kst-u@mib.org> - 2019-09-17 13:28 -0700
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 15:31 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 22:16 +0100
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 16:42 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:05 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:45 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 18:14 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 12:36 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 19:45 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 20:09 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 14:14 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:59 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 11:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 13:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 12:01 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 07:35 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 10:02 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:25 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:41 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:56 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 21:34 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:42 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-19 17:54 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 13:26 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:06 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:37 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:07 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:04 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 17:32 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:10 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:33 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:05 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:48 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 18:00 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 08:52 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-20 00:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 10:11 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:25 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:54 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:15 -0600
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:13 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:54 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:09 -0500
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:45 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:34 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 14:58 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:57 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 18:10 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-20 13:18 +0100
Re: Provably unprovable eliminates incompleteness Louis Valence <lvalence@example.com> - 2019-09-09 17:43 -0300
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:28 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:04 -0500
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 09:57 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-09 13:30 -0700
Re: Provably unprovable eliminates incompleteness temakoutera62@gmail.com - 2019-09-11 17:31 -0700
Page 12 of 13 — ← Prev page 1 … 10 11 [12] 13 Next page →
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 16:05 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <m6ydnRawy53gcB7AnZ2dnUU7-KvNnZ2d@giganews.com> |
| In reply to | #19341 |
On 9/19/2019 3:33 PM, Siri Cruise wrote: > In article <O9udnZdFPogAkBzAnZ2dnUU7-c3NnZ2d@giganews.com>, > peteolcott <Here@Home> wrote: > >> Keith Thompson proves that he fully understands the Infinitesimal >> number system: >> >> On 9/16/2019 11:38 PM, Keith Thompson wrote: >> > I can imagine that *this* set has a least element. For example >> > we can define "iota" as an infinitesimal, something that is not a >> > real number but that has a location on the number line, directly >> > adjacent to the real number 0. It is greater than 0 and less than >> > any positive real number. > > iota > iota^2 > iota^3 > ... > >> He elaborates this understanding much more completely in his >> 9/16/2019 11:38 PM, reply. > > Infinitesimals cannot be reals. A couple of centuries ago it was shown this > leads to inconsistency. Recently nonstandard analysis has reintroduced > infinitesimals and their reciprocals. Positive infinitesimals are an infinite > set each greater than zero and less than any positive real. Their reciprocals > are greater than any real number and defined since infinitesimals are nonzero. > > Note that for an infinitesimal dx, dx > dx^2 > dx^3 > ... . So with the usual < > infinitesimals also lack a minimum element. Choice assumes an order exists, but > we haven't found it. > This is the Pete Olcott copyright 2018, 2019 notion of infinitesimals that have a bijection to every point on the number line indexed by integers. Reals have no point immediately adjacent to 0.0, infinitesimals name this point 0.0[1]. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 15:48 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <chine.bleu-8634C2.15480719092019@reader.eternal-september.org> |
| In reply to | #19343 |
In article <m6ydnRawy53gcB7AnZ2dnUU7-KvNnZ2d@giganews.com>,
peteolcott <Here@Home> wrote:
> Reals have no point immediately adjacent to 0.0, infinitesimals
> name this point 0.0[1].
For positive reals exponents can be any reals, so that you can have a
nondenumerable semi-open set of exponents A = [1, oo) and thus a nondenumerable
semiopen set for real x X(x) = {x^a: 0<x<1, a in A} which has no minimum under <
and a maximium of x. This is a nondenumerable version of an infinite strictly
decreasing bounded sequence.
To maintain definitions of exponentiation and less than for surreal
infinitesimals, X(dx) for infinitesimal dx is also a nondenumerable subset of
(0, dx]; thus a nondenumerable set separates 0.0 and dx. There is no point
immediately adjacent to 0.0 even for surreals.
You can, of course, define a set of infinitesimals which are not surreal, but it
becomes your responsibility to prove your element 0.0[1] uniquely exists and can
be meaningfully orderred among reals.
I can define the set of all four corner triangles. However it is empty: it has
no (unique) elements.
I can also define < on naturals and < on triangles but that alone does not make
4 < triangle ABC a meaningful statement.
--
:-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @
'I desire mercy, not sacrifice.' /|\
The first law of discordiamism: The more energy This post / \
to make order is nore energy made into entropy. insults Islam. Mohammed
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 18:00 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <56mdnaI58e4HlRnAnZ2dnUU7-UXNnZ2d@giganews.com> |
| In reply to | #19350 |
On 9/19/2019 5:48 PM, Siri Cruise wrote:
> In article <m6ydnRawy53gcB7AnZ2dnUU7-KvNnZ2d@giganews.com>,
> peteolcott <Here@Home> wrote:
>
>> Reals have no point immediately adjacent to 0.0, infinitesimals
>> name this point 0.0[1].
>
> For positive reals exponents can be any reals, so that you can have a
> nondenumerable semi-open set of exponents A = [1, oo) and thus a nondenumerable
> semiopen set for real x X(x) = {x^a: 0<x<1, a in A} which has no minimum under <
> and a maximium of x. This is a nondenumerable version of an infinite strictly
> decreasing bounded sequence.
>
> To maintain definitions of exponentiation and less than for surreal
> infinitesimals, X(dx) for infinitesimal dx is also a nondenumerable subset of
> (0, dx]; thus a nondenumerable set separates 0.0 and dx. There is no point
> immediately adjacent to 0.0 even for surreals.
>
> You can, of course, define a set of infinitesimals which are not surreal, but it
> becomes your responsibility to prove your element 0.0[1] uniquely exists and can
> be meaningfully orderred among reals.
>
> I can define the set of all four corner triangles. However it is empty: it has
> no (unique) elements.
>
> I can also define < on naturals and < on triangles but that alone does not make
> 4 < triangle ABC a meaningful statement.
>
I don't pay any attention to any of these things. I simply derived a
notational convention that allows all of the adjacent points on a number
line to be directly referenced.
I also proved why this is required in that Real numbers leave gaps
in the number line with points that are unaccounted for.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2019-09-20 08:52 +0200 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm1svn$qe1$1@dont-email.me> |
| In reply to | #19352 |
On 20/09/2019 01:00, peteolcott wrote: > I don't pay any attention to any of these things. I simply derived a > notational convention that allows all of the adjacent points on a number > line to be directly referenced. You don't seem to pay attention to anything much. Making up a notation is not the same as forming a mathematical theory. > > I also proved why this is required in that Real numbers leave gaps > in the number line with points that are unaccounted for. > You haven't proven anything. "Proof by repeated assertion" is not valid in mathematics. Perhaps the real people could give up this thread? I had hoped that there might be some interesting mathematics here, or even that PO could learn something. But while we have seen that there are people in c.l.c++ who are competent and interested in mathematics, I don't think there is anyone here with a hammer big enough to knock some sense through PO's thick skull. And his continued wilful ignorance makes it difficult to have an intelligent discussion on the topic (or anything else).
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-20 00:10 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <chine.bleu-44F062.00101520092019@reader.eternal-september.org> |
| In reply to | #19356 |
In article <qm1svn$qe1$1@dont-email.me>, David Brown <david.brown@hesbynett.no> wrote: > > I also proved why this is required in that Real numbers leave gaps > > in the number line with points that are unaccounted for. > > > > You haven't proven anything. "Proof by repeated assertion" is not valid > in mathematics. Infinity is counterintuitive. Nondenumerable infinite sets are doubleplus counterinitutive. God made integers; all else is the work of man. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2019-09-20 10:11 +0200 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm21jo$igm$1@dont-email.me> |
| In reply to | #19357 |
On 20/09/2019 09:10, Siri Cruise wrote: > In article <qm1svn$qe1$1@dont-email.me>, David Brown <david.brown@hesbynett.no> > wrote: > >>> I also proved why this is required in that Real numbers leave gaps >>> in the number line with points that are unaccounted for. >>> >> >> You haven't proven anything. "Proof by repeated assertion" is not valid >> in mathematics. > > Infinity is counterintuitive. Nondenumerable infinite sets are doubleplus > counterinitutive. And the difference between infinite ordinals and infinite cardinals makes it even worse! > God made integers; all else is the work of man. > I remember making Peano integers in a Haskell-like functional programming language. First year maths students made the integers - all else is the work of second or third year students!
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| From | Juha Nieminen <nospam@thanks.invalid> |
|---|---|
| Date | 2019-09-20 08:25 +0000 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qm22dj$1j6s$1@adenine.netfront.net> |
| In reply to | #19343 |
In comp.lang.c++ peteolcott <Here@home> wrote: > This is the Pete Olcott copyright 2018, 2019 notion of > infinitesimals that have a bijection to every point on > the number line indexed by integers. > > Reals have no point immediately adjacent to 0.0, infinitesimals > name this point 0.0[1]. So you take an uncountable set, the set of reals, you add numbers to that set, and that somehow magically makes the set countable. And your proof of that is a simple assertion. You can't even provide a bijection between this expanded set of reals of yours, and the natural numbers. But surely it must be countable because you say it is. That's all the proof you need. Also, you can't give a single property of that "0.0[1]" number which distinguishes it from zero.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 09:54 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <n9-dnX44ueOHP-LAnZ2dnUU7-fvNnZ2d@giganews.com> |
| In reply to | #19182 |
On 9/15/2019 3:09 AM, Juha Nieminen wrote:
> In comp.lang.c++ peteolcott <Here@home> wrote:
>> On 9/13/2019 3:14 AM, Juha Nieminen wrote:
>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>> There is a contiguous set of points between (3.0, 4.0].
>>>> There is a first point in that interval, let's call it X.
>>>
>>> No, there isn't. Such a point doesn't exist.
>>>
>>> Learn some number theory, will you?
>>>
>>
>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!!
>>
>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment
>
> You are right and I'm wrong, even though that website does not
> say what you are saying?
>
> It doesn't matter how many arguments you present or how much you
> shout, it will not make "the smallest real number larger than 3"
> to start to exist.
>
The length of this interval is exactly 3.0
(0.0, 3.0]
The smallest real number larger than 0.0 is its first point.
The length of this interval is exactly one geometric point longer than 3.0
[0.0, 3.0]
If we limit the specified points in the intervals to integers then:
(0.0, 3.0] specifies: {1,2,3}
[0.0, 3.0] specifies: {0,1,2,3}
Proving that the above intervals are not the same length.
> In fact, even if you limit yourself to rational numbers, it still
> doesn't exist. There is no "smallest rational number larger than 3".
>
> Infinitesimals, no matter how you define them, do not help here.
> Such a number still doesn't exist, even if you include infinitesimals
> into your number system.
>
> Removing one number from an interval of real (or even rational) numbers
> doesn't make that number exist. You can remove an infinite amount of
> numbers from that interval, and it still doesn't make such a number
> to exist.
>
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-16 09:15 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Message-ID | <qlo8uj$db7$2@dont-email.me> |
| In reply to | #19187 |
On 2019-09-16 8:54 a.m., peteolcott wrote:
> On 9/15/2019 3:09 AM, Juha Nieminen wrote:
>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>> On 9/13/2019 3:14 AM, Juha Nieminen wrote:
>>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>>> There is a contiguous set of points between (3.0, 4.0].
>>>>> There is a first point in that interval, let's call it X.
>>>>
>>>> No, there isn't. Such a point doesn't exist.
>>>>
>>>> Learn some number theory, will you?
>>>>
>>>
>>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!!
>>>
>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment
>>
>> You are right and I'm wrong, even though that website does not
>> say what you are saying?
>>
>> It doesn't matter how many arguments you present or how much you
>> shout, it will not make "the smallest real number larger than 3"
>> to start to exist.
>>
>
> The length of this interval is exactly 3.0
> (0.0, 3.0]
> The smallest real number larger than 0.0 is its first point.
>
> The length of this interval is exactly one geometric point longer than 3.0
> [0.0, 3.0]
And points are zero-dimensional. They have no length.
> If we limit the specified points in the intervals to integers then:
> (0.0, 3.0] specifies: {1,2,3}
> [0.0, 3.0] specifies: {0,1,2,3}
> Proving that the above intervals are not the same length.
Claims about the integers don't carry over to the reals. As a trivial
example, the integer 1 is not divisible by 2. The real number 1.0 is.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 13:13 -0700 |
| Message-ID | <chine.bleu-8A9BD0.13134619092019@reader.eternal-september.org> |
| In reply to | #19182 |
In article <qlkrir$1iva$1@adenine.netfront.net>, Juha Nieminen <nospam@thanks.invalid> wrote: > In fact, even if you limit yourself to rational numbers, it still > doesn't exist. There is no "smallest rational number larger than 3". You can enumerate rationals, E:rationals to naturals. Then define the order O to be xOy = E(x)<E(y). The smallest rational larger than 3 would be 4 or thereabouts. This might not be the most useful order but does show the axiom of choice works on rationals. Note that you define a total order on R^n: each real in the orderred n-tuples has a decimal representation. You can interleave the digits of the n reals into a single real and define the total order of R^n to be the usual < on this R^1 set of interleaved reals. Again not a particularly useful order, but it does prove you can total order R^n for any natural n. Once you understand tricks like this are allowed, you realise maybe there is some order on reals that satisfies the axiom of choice. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 12:54 -0700 |
| Message-ID | <chine.bleu-DF95D0.12540119092019@reader.eternal-september.org> |
| In reply to | #19135 |
In article <qlefjm$300c$1@adenine.netfront.net>, Juha Nieminen <nospam@thanks.invalid> wrote: > In comp.lang.c++ peteolcott <Here@home> wrote: > > The next real number after 3.0 is the geometric point on the number > > line that is immediately adjacent to 3.0 on its right side. This geometric > > point is an infinitesimally larger than 3.0: encoded as the first point in > > the interval: (3,4] > > That would be "the smallest real number larger than 3". Which does not > exist. Not for the usual < order. Someday someone might come up with an order that can do this. According the axiom of choice, it's out there. Somewhere. [X-Files theme music] Do you believe? -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 15:09 -0500 |
| Message-ID | <w7CdndBgRODKfR7AnZ2dnUU7-L_NnZ2d@giganews.com> |
| In reply to | #19336 |
On 9/19/2019 2:54 PM, Siri Cruise wrote: > In article <qlefjm$300c$1@adenine.netfront.net>, > Juha Nieminen <nospam@thanks.invalid> wrote: > >> In comp.lang.c++ peteolcott <Here@home> wrote: >>> The next real number after 3.0 is the geometric point on the number >>> line that is immediately adjacent to 3.0 on its right side. This geometric >>> point is an infinitesimally larger than 3.0: encoded as the first point in >>> the interval: (3,4] >> >> That would be "the smallest real number larger than 3". Which does not >> exist. > > Not for the usual < order. Someday someone might come up with an order that can > do this. According the axiom of choice, it's out there. Somewhere. > > [X-Files theme music] Do you believe? > As explained in this reply On 9/19/2019 2:58 PM, peteolcott wrote: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] There is no such real number, because all Reals are divisible by 2 there is such an Infinitesimal number: a single indivisible point on the number line. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 12:45 -0700 |
| Message-ID | <chine.bleu-262ED3.12445219092019@reader.eternal-september.org> |
| In reply to | #19096 |
In article <pMqdnQFBSMfCXurAnZ2dnUU7-d3NnZ2d@giganews.com>, peteolcott <Here@Home> wrote: > The next real number after 3.0 is the geometric point on the number > line that is immediately adjacent to 3.0 on its right side. This geometric > point is an infinitesimally larger than 3.0: encoded as the first point in > the interval: (3,4] The axiom of choice says the set has a distinguished minimum with respect to some orderring, but not what that orderring is. The usual < order does not work; nobody has yet discoverred an orderring that does. Assuming choice produces unsettling results like this, but not inconsistencies, so it is allowed. Real numbers do not have infinitesimals. That was discoverred a couple of hundred years of ago. This is why most treatments of calculus use limits instead of the infinitesimals of Newton and Liebniz. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 12:34 -0700 |
| Message-ID | <chine.bleu-49A5CC.12343319092019@reader.eternal-september.org> |
| In reply to | #19089 |
In article <T9mdnX__WZbR9OvAnZ2dnUU7-R_NnZ2d@giganews.com>, peteolcott <Here@Home> wrote: > The number of real numbers is the number of adjacent geometric > points on a number line, countable using integers. You're misreading the axiom of choice. While the axiom can be assumed for nondenumerable sets, no has come up with an orderring of, say, reals that an open set has a distinguished minimum. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 14:58 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] |
| Message-ID | <UuadneUXFb9XQB7AnZ2dnUU7-dHNnZ2d@giganews.com> |
| In reply to | #19334 |
On 9/19/2019 2:34 PM, Siri Cruise wrote:
> In article <T9mdnX__WZbR9OvAnZ2dnUU7-R_NnZ2d@giganews.com>,
> peteolcott <Here@Home> wrote:
>
>> The number of real numbers is the number of adjacent geometric
>> points on a number line, countable using integers.
>
> You're misreading the axiom of choice. While the axiom can be assumed for
> nondenumerable sets, no has come up with an orderring of, say, reals that an
> open set has a distinguished minimum.
>
I have updated this on the basis of feedback:
(1) There cannot be a real number associated with the point
immediately adjacent to 0.0 because real numbers must be divisible
by 2 and single points are indivisible.
(2) If there is no real number immediately adjacent to 0.0 then
there is always a measurable gap after 0.0. By dividing the
size of the gap by 2 it gets smaller and smaller yet never closes,
there are always points in the gap that are unaccounted for.
This is where Infinitesimal numbers come in:
[0,1] - (0,1] = {0} a single point on the number line.
Thus proving a difference (in length) of one point between the first
interval and the second interval.
In all of the years where the width of a single point has been defined
to be 0 it was defined incorrectly, the actual width is Infinitesimal.
Infinitesimals sometimes act as if they had zero width and other times
act as if they minimum width. This is similar to the dichotomy of the
particle versus wave theories of light.
When we adapt (0,1] to the Infinitesimal number notational conventions it becomes
[0[1], 1] indicating an interval beginning with a single point offset from 0.
This notational convention allows us to reference subsequent immediately
adjacent points on the number line: [0[1], 1] - {0[1]} = [0[2], 1].
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 15:57 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] |
| Message-ID | <chine.bleu-31E44A.15574919092019@reader.eternal-september.org> |
| In reply to | #19337 |
In article <UuadneUXFb9XQB7AnZ2dnUU7-dHNnZ2d@giganews.com>,
peteolcott <Here@Home> wrote:
> This is where Infinitesimal numbers come in:
> [0,1] - (0,1] = {0} a single point on the number line.
> Thus proving a difference (in length) of one point between the first
> interval and the second interval.
You have to provide a length function and prove its properties. The best I can
think of is d(S) = d(inf S, sup S). Since inf[0, 1] = inf(0, 1], under my
definition d[0, 1] = d(0, 1].
I switch min to inf because you end up with lim d(x, 1], x/=0, x->0, and that's
just a cladded definition of inf.
--
:-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @
'I desire mercy, not sacrifice.' /|\
The first law of discordiamism: The more energy This post / \
to make order is nore energy made into entropy. insults Islam. Mohammed
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 18:10 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] |
| Message-ID | <NsOdndelnftYlxnAnZ2dnUU7-dXNnZ2d@giganews.com> |
| In reply to | #19351 |
On 9/19/2019 5:57 PM, Siri Cruise wrote:
> In article <UuadneUXFb9XQB7AnZ2dnUU7-dHNnZ2d@giganews.com>,
> peteolcott <Here@Home> wrote:
>
>> This is where Infinitesimal numbers come in:
>> [0,1] - (0,1] = {0} a single point on the number line.
>> Thus proving a difference (in length) of one point between the first
>> interval and the second interval.
>
> You have to provide a length function and prove its properties. The best I can
> think of is d(S) = d(inf S, sup S). Since inf[0, 1] = inf(0, 1], under my
> definition d[0, 1] = d(0, 1].
>
> I switch min to inf because you end up with lim d(x, 1], x/=0, x->0, and that's
> just a cladded definition of inf.
>
I don't understand any of that stuff.
I do understand that (0, 1] is one point longer than (0, 1).
Which entails that the definition of zero width points is incorrect.
The first interval clearly has one more point than the second.
The first interval also has a length of exactly 1.0 and the
second interval has a length that is one point less than 1.0
because the missing point clearly has a numerical value that
is greater than its predecessor.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> |
|---|---|
| Date | 2019-09-20 13:18 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] |
| Message-ID | <fs3hF.14183$DK.10262@fx21.fr7> |
| In reply to | #19353 |
On 20/09/2019 00:10, peteolcott wrote:
> On 9/19/2019 5:57 PM, Siri Cruise wrote:
>> In article <UuadneUXFb9XQB7AnZ2dnUU7-dHNnZ2d@giganews.com>,
>> peteolcott <Here@Home> wrote:
>>
>>> This is where Infinitesimal numbers come in:
>>> [0,1] - (0,1] = {0} a single point on the number line.
>>> Thus proving a difference (in length) of one point between the first
>>> interval and the second interval.
>>
>> You have to provide a length function and prove its properties. The best
>> I can
>> think of is d(S) = d(inf S, sup S). Since inf[0, 1] = inf(0, 1], under my
>> definition d[0, 1] = d(0, 1].
>>
>> I switch min to inf because you end up with lim d(x, 1], x/=0, x->0, and
>> that's
>> just a cladded definition of inf.
>>
>
> I don't understand any of that stuff.
> I do understand that (0, 1] is one point longer than (0, 1).
>
> Which entails that the definition of zero width points is incorrect.
> The first interval clearly has one more point than the second.
Your assertion in the form of an erroneous premise followed by an equally
erroneous conclusion is, obviously, also erroneous. You don't get to
define what is meant by a "geometric point"; we already have a well
established and accepted definition for that concept.
>
> The first interval also has a length of exactly 1.0 and the
> second interval has a length that is one point less than 1.0
> because the missing point clearly has a numerical value that
> is greater than its predecessor.
More erroneous nonsense.
You are either:
1) a troll;
2) a fucktard;
or
3) not taking your medication.
Which is it?
/Flibble
--
"Snakes didn't evolve, instead talking snakes with legs changed into
snakes." - Rick C. Hodgin
“You won’t burn in hell. But be nice anyway.” – Ricky Gervais
“I see Atheists are fighting and killing each other again, over who
doesn’t believe in any God the most. Oh, no..wait.. that never happens.” –
Ricky Gervais
"Suppose it's all true, and you walk up to the pearly gates, and are
confronted by God," Bryne asked on his show The Meaning of Life. "What
will Stephen Fry say to him, her, or it?"
"I'd say, bone cancer in children? What's that about?" Fry replied.
"How dare you? How dare you create a world to which there is such misery
that is not our fault. It's not right, it's utterly, utterly evil."
"Why should I respect a capricious, mean-minded, stupid God who creates a
world that is so full of injustice and pain. That's what I would say."
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| From | Louis Valence <lvalence@example.com> |
|---|---|
| Date | 2019-09-09 17:43 -0300 |
| Message-ID | <86v9u1gpzn.fsf@example.com> |
| In reply to | #19087 |
Stuart Redmann <DerTopper@web.de> writes: > Dhu on Gate <campbell@neotext.ca> wrote: [...] >> Since this is unreadable by peons, I can only speculate, >> but provably unprovable sounds like a useless tautology. >> >> Dhu > > It isn't. It rather shows that - like the speed of light in physics - there > are some rather unexpected limitations to what is possible in mathematics. > For many years mathematicians believed that, given a set of axioms, every > possible theorem in the given field can be proven to be either true or > false based on logical deduction from these axioms. > > Goedel showed that this is not always the case (see the continuum > hypothesis). This implies that there are things in mathematics that cannot > be proven. This culminated in Goedels incompleteness theorem, which is > considered by many mathematicians as a severe throwback in maths. Despite my very limited understanding of logic, mathematics and everything else, I can't agree with you. There are some limitations to what is possible in formal logic; the same cannot today be said about mathematics. There are things in some formal logic systems that cannot be proven, but AFAIK there is no known result to the effect of what mathematics can or cannot prove. Peter Smith in ``An Introduction to Godel's Theorems (ISBN: 978-0-511-35096-2)'', on section 1.2, page, writes: --8<---------------cut here---------------start------------->8--- Suppose we try to specify a suitable axiomatic theory T that seems to capture the structure of the natural number sequence and pin down addition and multiplication (and maybe a lot more besides). Then Godel gives us a recipe for coming up with a corresponding sentence G(T), couched in the language of basic arithmetic, such that (i) we can show (on very modest assumptions, e.g. that T is consistent) that neither G(T) nor ~G(T) can be derived in T, and yet (ii) we can also recognize that, at least if T is consistent, G(T) will be true. --8<---------------cut here---------------end--------------->8--- So, Godel's recipe itself shows T is incomplete, meaning T cannot prove (as true or false) everything that can be stated in T. One could think that, therefore, we don't know whether the statement G(T) is true or false. Peter Smith adds that we can also recognize that, assuming T is consistent, then G(T) will be true. This /recognition/ is not backed up by T because T only asserts what it can --- and T cannot assert G(T). We may say we have a precise definition of a system of logic is, but we cannot say we have a precise definition of what mathematics is. What we can say is that if mathematics can be perfectly equated to logic, then we don't have any idea of what this system of logic would be to be equated to what we think mathematics is.
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| From | Siri Cruise <chine.bleu@yahoo.com> |
|---|---|
| Date | 2019-09-19 12:28 -0700 |
| Message-ID | <chine.bleu-8BD625.12284619092019@reader.eternal-september.org> |
| In reply to | #19087 |
In article <581781046.589713241.741596.DerTopper-web.de@news.eternal-september.org>, Stuart Redmann <DerTopper@web.de> wrote: > Goedel showed that this is not always the case (see the continuum > hypothesis). This implies that there are things in mathematics that cannot > be proven. This culminated in Goedels incompleteness theorem, which is > considered by many mathematicians as a severe throwback in maths. Goedel's incompleteness theorem is not that a specific proposition is unprovable but that any system complex enough to prove number theory theorems will have either true propositions which cannot be proven (incompleteness) or false propositions which can be proven (w-inconsistency). Picture the boundary between truth and falseness as if a fractal curve, truth and falseness become so entangled that it takes a nondenumerably infinite proof to distinguish. We can force the issue on a finite subset of propositions asserted or denied as postulates without introducing inconsistency. Experience has shown the continuum hypothesis like the parallel postulates does not lead to inconsistency. -- :-<> Siri Seal of Disavowal #000-001. Disavowed. Denied. Deleted. @ 'I desire mercy, not sacrifice.' /|\ The first law of discordiamism: The more energy This post / \ to make order is nore energy made into entropy. insults Islam. Mohammed
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